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Popular Calculus Problems

(\partial)/(\partial x)(ln(5x^2+y^2+9))	\frac{\partial\:}{\partial\:x}(\ln(5x^{2}+y^{2}+9))
(d^2y)/(dx^2)-5(dy)/(dx)+6y=0	\frac{d^{2}y}{dx^{2}}-5\frac{dy}{dx}+6y=0
derivative of f(x)=(22)/((1-x)^3)	derivative\:f(x)=\frac{22}{(1-x)^{3}}
normal of y=x^2-2x,(3,3)	normal\:y=x^{2}-2x,(3,3)
(dy}{dx}=\frac{x^2)/9+7/9	\frac{dy}{dx}=\frac{x^{2}}{9}+\frac{7}{9}
integral of ((x^2-4x+4))/(x-2)	\int\:\frac{(x^{2}-4x+4)}{x-2}dx
y^{''}=8(y^')^2	y^{\prime\:\prime\:}=8(y^{\prime\:})^{2}
area y=e^x,y=e^{-2x},x=ln(3)	area\:y=e^{x},y=e^{-2x},x=\ln(3)
derivative of (cos(x)^2-2sin(x))	\frac{d}{dx}((\cos(x))^{2}-2\sin(x))
tangent of y= 6/(sin(x)+cos(x)),(0,6)	tangent\:y=\frac{6}{\sin(x)+\cos(x)},(0,6)
limit as x approaches 1+of 4/(2x-2)	\lim\:_{x\to\:1+}(\frac{4}{2x-2})
(\partial)/(\partial x)(x^2-2x-xy)	\frac{\partial\:}{\partial\:x}(x^{2}-2x-xy)
limit as x approaches infinity of (ln(x^5))/(13x)	\lim\:_{x\to\:\infty\:}(\frac{\ln(x^{5})}{13x})
(\partial)/(\partial x)(e^{-x/y})	\frac{\partial\:}{\partial\:x}(e^{-\frac{x}{y}})
integral of pi(2x)^2	\int\:π(2x)^{2}dx
derivative of 4cos(x+4sin(x))	\frac{d}{dx}(4\cos(x)+4\sin(x))
derivative of 2xsin(x)+cos(x)x^2	derivative\:2x\sin(x)+\cos(x)x^{2}
laplacetransform-2t^2	laplacetransform\:-2t^{2}
integral of 4e^{-4x}	\int\:4e^{-4x}dx
derivative of x/(1-ln(x-5))	derivative\:\frac{x}{1-\ln(x-5)}
integral from 0 to (5pi)/4 of 3tan(x/5)	\int\:_{0}^{\frac{5π}{4}}3\tan(\frac{x}{5})dx
sum from n=0 to infinity of 1/(n^2+1)	\sum\:_{n=0}^{\infty\:}\frac{1}{n^{2}+1}
implicit (dy)/(dx),y=7^x	implicit\:\frac{dy}{dx},y=7^{x}
sum from n=0 to infinity of (1^n)/(4^n)	\sum\:_{n=0}^{\infty\:}\frac{1^{n}}{4^{n}}
(3x-2)^'	(3x-2)^{\prime\:}
limit as x approaches 3+of (5x)/(x-3)	\lim\:_{x\to\:3+}(\frac{5x}{x-3})
tangent of f(x)= 6/(3x+1),\at x=-1	tangent\:f(x)=\frac{6}{3x+1},\at\:x=-1
derivative of y=(0.9e^x)/(tan(x))	derivative\:y=\frac{0.9e^{x}}{\tan(x)}
f(x)=-4sin(2x)+3cos(3x)	f(x)=-4\sin(2x)+3\cos(3x)
integral of (x^3-4x^2-4x+20)/(x^2-5)	\int\:\frac{x^{3}-4x^{2}-4x+20}{x^{2}-5}dx
derivative of f(x)=8e^{-x}+e^{3x}	derivative\:f(x)=8e^{-x}+e^{3x}
inverse oflaplace (s+1)/(s^2)	inverselaplace\:\frac{s+1}{s^{2}}
derivative of f(x)=1x^3	derivative\:f(x)=1x^{3}
derivative of 8sin((2pi/3))	\frac{d}{dx}(8\sin(\frac{2π}{3}))
integral of (2x)/(3x-5)	\int\:\frac{2x}{3x-5}dx
sum from n=1 to infinity of (n+2)/(n+1)	\sum\:_{n=1}^{\infty\:}\frac{n+2}{n+1}
integral of ((1-cos^3(x))sin(x))	\int\:((1-\cos^{3}(x))\sin(x))dx
integral of (sin^9(x))cos(x)	\int\:(\sin^{9}(x))\cos(x)dx
limit as x approaches 0 of (sin(6x))/x	\lim\:_{x\to\:0}(\frac{\sin(6x)}{x})
integral of λe^{-λx}	\int\:λe^{-λx}dx
integral of 2sin(2t)	\int\:2\sin(2t)dt
limit as z approaches 1 of (z-1)/(z^2-1)	\lim\:_{z\to\:1}(\frac{z-1}{z^{2}-1})
integral from 0 to pi/6 of xtan^2(2x)	\int\:_{0}^{\frac{π}{6}}x\tan^{2}(2x)dx
limit as x approaches 0 of e^{3x}-1-3x	\lim\:_{x\to\:0}(e^{3x}-1-3x)
derivative of 1/(4x^4)	derivative\:\frac{1}{4x^{4}}
(dy)/(dx)=4(x^2+1),x(pi/4)=1	\frac{dy}{dx}=4(x^{2}+1),x(\frac{π}{4})=1
integral of (8x^3+1/(x^2))	\int\:(8x^{3}+\frac{1}{x^{2}})dx
tangent of y=2^{-x},(-1,2)	tangent\:y=2^{-x},(-1,2)
derivative of 1-4cos(x)	\frac{d}{dx}(1-4\cos(x))
integral from-2 to 2 of 1/(x^2-9)	\int\:_{-2}^{2}\frac{1}{x^{2}-9}dx
integral of tan^4(xse)c^2x	\int\:\tan^{4}(xse)c^{2}xdx
integral of ((3+ln(2x))^3)/x	\int\:\frac{(3+\ln(2x))^{3}}{x}dx
(dv)/(dt)=9.8-v	\frac{dv}{dt}=9.8-v
f(x)=xe^{2x^2-4x}	f(x)=xe^{2x^{2}-4x}
y^{''}+4y^'+5y=-15x+5e^{-x}	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=-15x+5e^{-x}
derivative of (x^3)/3-(x^2)/2-2x	derivative\:\frac{x^{3}}{3}-\frac{x^{2}}{2}-2x
derivative of e^{3x}-1	\frac{d}{dx}(e^{3x}-1)
integral from 2 to 4 of (x+y)/(55)	\int\:_{2}^{4}\frac{x+y}{55}dy
integral of (x(x-8))/((x-4)^3)	\int\:\frac{x(x-8)}{(x-4)^{3}}dx
2(2x^2+y^2)dx-xydy=0	2(2x^{2}+y^{2})dx-xydy=0
derivative of f(x)=(x-5)/(x+3)	derivative\:f(x)=\frac{x-5}{x+3}
tangent of f(x)=5x^2-2x+4	tangent\:f(x)=5x^{2}-2x+4
limit as x approaches-4+of (-1)/(x^2-16)	\lim\:_{x\to\:-4+}(\frac{-1}{x^{2}-16})
limit as x approaches 1 of (2x-7)/(4x+5)	\lim\:_{x\to\:1}(\frac{2x-7}{4x+5})
inverse oflaplace 2/(s-2)	inverselaplace\:\frac{2}{s-2}
integral of (-x^2+2x-8)/((x^2+4)(x-2))	\int\:\frac{-x^{2}+2x-8}{(x^{2}+4)(x-2)}dx
integral of x^2sqrt(4x+7)	\int\:x^{2}\sqrt{4x+7}dx
integral of (x^2+10x)cos(x)	\int\:(x^{2}+10x)\cos(x)dx
derivative of arcsinh(x^2)	\frac{d}{dx}(\arcsinh(x^{2}))
derivative of y=((e^x))/x	derivative\:y=\frac{(e^{x})}{x}
integral of (2x)/(x^2-6)	\int\:\frac{2x}{x^{2}-6}dx
derivative of sqrt((6x-5/(10x+7)))	\frac{d}{dx}(\sqrt{\frac{6x-5}{10x+7}})
taylor ln(x),8	taylor\:\ln(x),8
laplacetransform t^3e^{-t}	laplacetransform\:t^{3}e^{-t}
derivative of 1/3 arctan(x/3)	derivative\:\frac{1}{3}\arctan(\frac{x}{3})
sum from n=0 to infinity of 1/(6n+5)	\sum\:_{n=0}^{\infty\:}\frac{1}{6n+5}
derivative of 2e^{-4x^2+3x+7}	\frac{d}{dx}(2e^{-4x^{2}+3x+7})
derivative of f(x)= 7/(sqrt(t))	derivative\:f(x)=\frac{7}{\sqrt{t}}
derivative of ln((4x/(x+9)))	\frac{d}{dx}(\ln(\frac{4x}{x+9}))
integral from 0 to 2 of sqrt(1+9x)	\int\:_{0}^{2}\sqrt{1+9x}dx
integral from 6 to 9 of 1/(9+(x-6)^2)	\int\:_{6}^{9}\frac{1}{9+(x-6)^{2}}dx
derivative of x+c	\frac{d}{dx}(x+c)
derivative of x^4sin(xcos(x))	\frac{d}{dx}(x^{4}\sin(x)\cos(x))
integral from 0 to 1 of 6^x	\int\:_{0}^{1}6^{x}dx
tangent of y=x^3-3x+1,(3,19)	tangent\:y=x^{3}-3x+1,(3,19)
derivative of In(xsqrt(x^2-1))	\frac{d}{dx}(In(x\sqrt{x^{2}-1}))
integral of tan^5(3θ)	\int\:\tan^{5}(3θ)dθ
derivative of ln((sqrt(x+1))/(x^2+4))	derivative\:\ln(\frac{\sqrt{x+1}}{x^{2}+4})
tangent of f(x)=3-2cos(x),\at x= pi/2	tangent\:f(x)=3-2\cos(x),\at\:x=\frac{π}{2}
integral of 2/(x^2+1)	\int\:\frac{2}{x^{2}+1}dx
f(x)=(sqrt(x+5))/(sqrt(x+2))	f(x)=\frac{\sqrt{x+5}}{\sqrt{x+2}}
integral of 1/(x*sqrt(x^2-1))	\int\:\frac{1}{x\cdot\:\sqrt{x^{2}-1}}dx
(\partial)/(\partial x)(y^4)	\frac{\partial\:}{\partial\:x}(y^{4})
derivative of (4x/(x+3))	\frac{d}{dx}(\frac{4x}{x+3})
(dy)/(dx)= x/(x^2+4)	\frac{dy}{dx}=\frac{x}{x^{2}+4}
(dy)/(dx)=5y^2cos(x)	\frac{dy}{dx}=5y^{2}\cos(x)
integral of 10xln(5x)	\int\:10x\ln(5x)dx
integral from 0 to 2 of 4x^2-x^4	\int\:_{0}^{2}4x^{2}-x^{4}dx
integral from 1 to infinity of xe^{-5x}	\int\:_{1}^{\infty\:}xe^{-5x}dx
integral of (4x^3)/(x^2)	\int\:\frac{4x^{3}}{x^{2}}dx

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